No. Rebrandly only tracks conversions from visitors who arrived via a Rebrandly branded link. Conversions from other traffic sources (direct visits, organic search, email, ads on other platforms, etc.) won't appear in your conversion tracking reports.
What you'll see: Only conversions attributed to clicks on your tracked Rebrandly links.
What you won't see: Conversions from visitors who didn't click a Rebrandly link to get to your site.
This is because Rebrandly's conversion tracking connects clicks to conversions, so it only measures the impact of your branded links. This means you can run a very focused campaign with branded links distributed in a strategic way, and then measure your efforts with the tracking data in Rebrandly.
For a complete view of all conversions on your site, you'll need to use web analytics tools like Google Analytics alongside Rebrandly.